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1. Majorization Minimization Methods for Distributed Pose Graph Optimization

   https://doi.org/10.1109/TRO.2023.3324818  

   Fan, Taosha; Murphey, Todd D. (October 2023, IEEE Transactions on Robotics)

   We consider the problem of distributed pose graph optimization (PGO) that has important applications in multi- robot simultaneous localization and mapping (SLAM). We pro- pose the majorization minimization (MM) method for distributed PGO (MM−PGO) that applies to a broad class of robust loss kernels. The MM−PGO method is guaranteed to converge to first-order critical points under mild conditions. Furthermore, noting that the MM−PGO method is reminiscent of proximal methods, we leverage Nesterov’s method and adopt adaptive restarts to accelerate convergence. The resulting accelerated MM methods for distributed PGO—both with a master node in the network (AMM−PGO∗) and without (AMM−PGO#)— have faster convergence in contrast to the MM−PGO method without sacrificing theoretical guarantees. In particular, the AMM−PGO# method, which needs no master node and is fully decentralized, features a novel adaptive restart scheme and has a rate of convergence comparable to that of the AMM−PGO∗ method using a master node to aggregate information from all the nodes. The efficacy of this work is validated through extensive applications to 2D and 3D SLAM benchmark datasets and comprehensive comparisons against existing state-of-the-art methods, indicating that our MM methods converge faster and result in better solutions to distributed PGO. The code is available at https://github.com/MurpheyLab/DPGO. 

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2. Generalized Proximal Methods for Pose Graph Optimization

   Fan, Taosha; Murphey, Todd (January 2019, Springer tracts in advanced robotics)

   null (Ed.)

   In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized proximal methods for PGO converge to first-order critical points. Furthermore, we propose methods that significantly accelerate the rates of convergence almost without loss of any theoretical guarantees. In addition, our proposed methods can be easily distributed and parallelized with no compromise of efficiency. The efficacy of this work is validated through implementation on simultaneous localization and mapping (SLAM) and distributed 3D sensor network localization, which indicate that our proposed methods are a lot faster than existing techniques to converge to sufficient accuracy for practical use. 

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3. Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation

   https://doi.org/10.1109/IROS40897.2019.8968044  

   Fan, Taosha; Wang, Hanlin; Rubenstein, Michael; Murphey, Todd (November 2019, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   In this paper, we present CPL-Sync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is more efficient and capable of solving planar PGO certifiably. The C++ code for CPL-Sync is available at https://github. com/fantaosha/CPL- Sync. 

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4. Active Rendezvous for Multi-Robot Pose Graph Optimization using Sensing over Wi-Fi

   https://doi.org/arXiv:1907.05538  

   Wang, W.; Jadhav, N.; Vohs, P.; Hughes, N.; Mazumder, M.; Gil, S. (January 2019, International symposium on robotics research (ISRR))

   We present a novel framework for collaboration amongst a team of robots performing Pose Graph Optimization (PGO) that addresses two important challenges for multi-robot SLAM: i) that of enabling information exchange "on-demand" via Active Rendezvous without using a map or the robot's location, and ii) that of rejecting outlying measurements. Our key insight is to exploit relative position data present in the communication channel between robots to improve groundtruth accuracy of PGO. We develop an algorithmic and experimental framework for integrating Channel State Information (CSI) with multi-robot PGO; it is distributed, and applicable in low-lighting or featureless environments where traditional sensors often fail. We present extensive experimental results on actual robots and observe that using Active Rendezvous results in a 64% reduction in ground truth pose error and that using CSI observations to aid outlier rejection reduces ground truth pose error by 32%. These results show the potential of integrating communication as a novel sensor for SLAM. 

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5. Parameter Selection by GCV and a \(\boldsymbol {\chi^2}\) Test within Iterative Methods for \(\boldsymbol{\ell_1}\)-Regularized Inverse Problems

   https://doi.org/10.1137/24M165805X  

   Sweeney, Brian; Renaut, Rosemary; Español, Malena I (May 2025, SIAM Journal on Scientific Computing)

   l1 regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the split Bregman and the majorization-minimization iterative methods that turn this nonsmooth minimization problem into a sequence of steps that include solving an -regularized minimization problem. We consider selecting the regularization parameter in the inner generalized Tikhonov regularization problems that occur at each iteration in these iterative methods. The generalized cross validation method and chi2 degrees of freedom test are extended to these inner problems. In particular, for the chi2 test this includes extending the result for problems in which the regularization operator has more rows than columns and showing how to use the -weighted generalized inverse to estimate prior information at each inner iteration. Numerical experiments for image deblurring problems demonstrate that it is more effective to select the regularization parameter automatically within the iterative schemes than to keep it fixed for all iterations. Moreover, an appropriate regularization parameter can be estimated in the early iterations and fixed to convergence. 

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